Why did the Twitch app move from its old Play Store listing at "tv.twitch.android.viewer" to a new one at "tv.twitch.android.app?" Beats me - maybe it's because the added functionality in version 4.0 makes it more of a "full" interface for the popular streaming game video service, as opposed to simply a viewer. You still can't stream video directly from your Android device, but now you've got access to the whole expansive collection of gameplay videos.
In particular, that includes previously-recorded video sessions and highlights, which used to be off-limits to the Android app for some reason. Twitch calls these "on-demand" videos, which is an odd way of classifying videos that aren't actually streaming live right at this moment. To access previously-recorded videos, tap the "Activity Feed" (the little film icon) in the lower left-hand corner of the video player on any channel.
Other than the extra video access and the new Play Store listing, there doesn't appear to be too much added in version 4.0. The app icon has had its white-on-purple color scheme switched for no particular reason that I can see, since the rest of the app interface (notably updated with a windowed player and an audio-only option two months ago) is otherwise unchanged.